I want one object to "chase" another object
Chase:





View from top - Ortho view

An empty is placed at the center of the red circle's intended orbit and rotates. The circle is parented to this
so it rotates around the empty.

A narrow and invisible plane is added and has it's pivot point set to it's upper end.  This is then located at the red circle's center (SH-S)  and will act a leash.

The leash is scaled in length and rotated so it's other end is at the stationary blue circle.

The blue circle is then parented to the leash choosing the "Vertex" option. (child = blue circle)

The leash's two end-vertices (at the blue circle) are then shapekeyed to shrink the leash over the same number of frames (minus a few) as it takes the red circle to make one orbit.  You can have this happen (the intercept) much sooner or over several orbits if you wish.

When played the red circle does it's orbit and the leash is forced to follow and rotate with it.
At the same time shapekeys are shrinking it's length, automatically making it close in on the red circle.



By adjusting the leash's shape key F curves in the Graph editor, the nature of the intercept can be varied to suit.